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A194377 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(6) and < > denotes fractional part. 3
1, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368. Although a(n)=A007957(n) for n = 1..70, the number 208, for example, is here but not A007957.

LINKS

Table of n, a(n) for n=1..76.

MATHEMATICA

r = Sqrt[6]; c = 1/2;

x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 500}];

Flatten[Position[t1, 1]]   (* empty *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];

Flatten[Position[t2, 1]]   (* A194376 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

Flatten[Position[t3, 1]]   (* A194377 *)

PROG

(PARI) is(n)=my(r=sqrt(6), f=x->x-x\1); sum(k=1, n, f(1/2+k*r)-f(k*r))>0 \\ Charles R Greathouse IV, Jul 25 2012

CROSSREFS

Cf. A007957, A194368, A194376.

Sequence in context: A249494 A047747 A007957 * A258432 A128938 A215138

Adjacent sequences:  A194374 A194375 A194376 * A194378 A194379 A194380

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified May 13 13:49 EDT 2021. Contains 343857 sequences. (Running on oeis4.)